# Tetration

### From charlesreid1

Tetration. A bit of background on what tetration is. This notation will let you write what are, unquestionably, the biggest numbers you've ever seen in your life.

Notation for progressively larger numbers.

5 tetrated can be written as 5 to the power of 5^5^5^5 mod 10, mod 11

Consider the number 4. To make a larger number out of 4, you might add 4 to 4 and get 8. You might multiply by 4 to get 16. Or you might raise 4 to the power of itself: 4^4, or 256. But what if you took that a step further: Raise 4 to the power of 4, 4 times:

That's 4 tetrated, or . That's a very, very, very big number:

And that's just FOUR tetrated.

Imagine 10 tetrated. 20, 30, 40 tetrated. 100 tetrated. A googol tetrated.

Time for a puzzle.

What is the remainder when you divide

by 11?

See also: the Knuth up arrow http://mathworld.wolfram.com/PowerTower.html

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